## 799. Increase Of The Focal Distance Of The Lens Due To Different Distances Of The Object

Increase Of The Focal Distance Of The Lens Due To Different Distances Of The Object. A certain distance exists for each lens, at and beyond which the parallaxes of the luminous points are so small that the incident rays may be considered to be parallel to each other. In this case the distinct image is situated in the principal focal plane of the lens - i. e., in the plane which is conjugate to infinitely distant objects. The subjoined table shows how far, in the case of our lenses, the distant image lies behind the principal focal plane when the object is situated at a finite (and rather short) distance from the lens.

800.

 No. of Lens 0 1 2 3 4 5 6 7 Focus in inches 4 3/4 6 7 8 1/2 9 1/2 10 3/4 12 14 Distance of Object in feet Distance of the Conjugate Focus beyond the Principal Focus in inches 1666............ .0012 .0020 .0028 .0036 .0048 .0060 .0072 .0104 333 ........... .0056 .0092 .0128 .0174 .0232 .0292 .0360 .0520 166 ........... .0116 .0180 .0260 .0352 0464 .0584 .0724 .1044 100 ........... .0192 .0300 .0436 .0592 .0776 .0980 .1212 .1748 66............ .0288 .0452 .0652 .0892 .1164 .1476 .1838 .2640 50............ .0388 .0604 .0872 .1192 .1560 .1980 .2448 .3540 40............ .0484 .0760 .1096 .1496 .1960 .2484 .3080 .444 33............ .0584 .0912 .1320 .1800 .2360 .2996 .3716 .536 30............ .0648 .1016 .1468 .2008 .2628 .3340 .412 .600 27............ .0732 .1144 .1656 .2264 .2968 .3772 .468 .680 23............ .0836 .1312 .1900 .2600 .3408 .432 .536 .780 20............ .0976 .1540 .2228 .3048 .4000 .508 .632 .920 17............ .1180 .1856 .2688 .3684 .4840 .616 .764 1.116 13............ .1484 .2336 .3392 .4640 .6120 .784 .972 1.424 10............ .2000 .3160 .4600 .6220 .8360 1.068 1.332 1.964 7............ .3064 .488 .7120 .9840 1.3080 1.684 2.116 3.160 3............ .656 1.060 1.5800 2.2320 1.0320 3.996 5.16 8.12

801. This table is very instructive. It shows, e. g., that lens No. 0, in the case of an object situated at a distance of 166 feet requires a displacement of only .0116 inch of the focusing screen (with respect to its position in the plane of the principal focus), whereas lens No. 7 requires this displacement when the object is at a distance of 1.666 feet. Since, with the rapidities ordinarily employed, a difference of .016 inches in the position of the focusing screen does not produce any sensible diffusion, we see from the table that lens No. 0 is capable of simultaneously sharply depicting objects situated at a distance beyond 50 feet; No. 7, those beyond 1,666 feet; No. 9, however, only those beyond 3,333 feet, etc. In general, the table shows that caeteris paribus, i. e., with the same relative apertures or with the same rapidities, the depth of focus rapidly diminishes as the focal length increases.

802. This table may be employed to sharply focus an object without the aid of the focusing screen, when the distance of the former is approximately ascertained by pacing off, or otherwise known.